ch 9 Flashcards
Annuity: a stream or series of equal payments to be received in the future.
Annuity: a stream or series of equal payments to be received in the future.
The payments are assumed to be received at the end of each period (unless stated otherwise).
A good example of an annuity is a lease, where a fixed monthly charge is paid over a number of years.
What will be the future value of $1,000 to be received at the end of each year for 4 years given a 10% interest rate?
PV= 0 PMT = -1000 I/Y= 10% N=4 FV=? 4641
What will be the future value of $1,000 to be received at the
beginning of each year for 4 years given a 10% interest rate?
pv=?= 3486.85 FV= 0 PMT= -1000 N= 4 I/Y=10 BGN KEY ON
Assuming we wish to accumulate $4,641 after four years at a 10% interest rate, how much do we need to set aside at the end of each of the four periods?
PV= 0 FV = -4641 PMT=?=1000 I/Y =10 N=4
A $10,000 investment will generate $1,490 a year for the next 10 years, what is the interest rate or yield on the investment?
PV= -1000 FV= 1464.10 PMT =0 N=4 I/Y= ? =10%
A problem may involve a combination of single amounts and an annuity. It is referred as a deferred annuity
Example:
What is the PV of an Annuity of $1,000 that will be paid at the end of each year from the fourth through the eight year, with a discount rate of 8 percent?
First, find the PV of the annuity of $1,000 being paid for 5 years beginning 4 years in the future with a discount rate of 8%
Next, find the PV of $3,992.71 to be received at the end of year 3 discounted back to the present with a discount rate of 8%
PV= ?= 3992.71 FV=0 N=5 I/Y=8 PMT=1000
PV= ? = 3169.54 FV= 3992.71 PMT= 0 I/Y =8 N=3
The formula for a perpetual annuity (with equal payments at the end of the period) is as follows:
PV= A = PMT
__ ____
i i
The formula for a perpetual annuity growing at a constant rate (g) is as follows:
PV= A
___
i - g
The formula for an annuity growing at a constant rate (g) for a limited period of time (n) is as follows:
It is common to have mortgages that have interest compounded semiannually, with payments made monthly.
Calculations of the monthly payment must acknowledge the early payment of interest.
A 20-year, $80,000 mortgage carries an annual interest rate of 8% compounded semiannually. How much is the monthly payment?
First, we calculate the monthly effective interest
Next, we calculate the monthly payment on the mortgage using the monthly effective interest rate
fv= 1.04 pv= -1.0 n=6 pmt =0 i=?= 0.6558% press 6 2nd EFF 4 = 3.9349
PV= -80000 FV= 0 N= 240 (20 YRS X12) I/Y= .6558 CPT PMT = 662.69
The financial manager uses the time value of money approach to value cash flows that occur at different points in time.
A dollar invested today at compound interest will grow to a larger value in future. That future value, discounted at compound interest, is equated to a present value today.
Cash payments may be received for an infinite period (perpetuity) in equal payments, or with payments growing at a constant rate.
A financial asset (security) is a claim against a firm, government or individual for future expected cash flows.
what are some examples
Examples of financial assets are bonds, preferred stocks and common stocks.
An investment decision should be made by:
comparing the price (or market value) of a financial asset to its present value.
determining the discount rate that equates the market value of a financial asset with the present value of its future expected cash flows.
This discount rate is the market-determined required rate of return (ROR) or yield.
The Required Real Rate of Return:
represents the opportunity cost of the investment
in the early 1990’s, 5-7%, but now about 2 to 3%
Inflation Premium:
a premium to compensate for the effects of inflation
Since 2000 slightly less than 2%
Risk Premium:
a premium associated with business and financial risk
default, liquidity and maturity risk
typically, 2-6%
